Pelosi sent Trump a letter on Wednesday, saying the US Secret Service, which is required to provide security for the speech, which is scheduled on January 29, has not received funding during the federal closure.
“Sadly, given the security concerns and unless government re-opens this week, I suggest that we work together to determine another suitable date after government has re-opened for this address or for you to consider delivering (it) in writing to the Congress on January 29th," Pelosi write in her letter, Presstv Reported.
The United States is experiencing its longest government shutdown in history, with about 25 percent of federal agencies and offices shuttered.
The Secret Service, which is charged with the protection of the president, provides security for what are known as national special security events, including the State of the Union.
The agency operates under the US Department of Homeland Security.
“Both the US Secret Service and the Department of Homeland Security have not been funded for 26 days now -– with critical departments hamstrung by furloughs," Pelosi noted in her letter.
The government shutdown was triggered by Trump’s demand for $5.7 billion to fund a wall along the US-Mexico border, which Democrats in Congress oppose.
Analysts are warning that the cost of keeping federal agencies closed down will soon surpass the amount that Trump has requested for his controversial wall.
Pelosi suggested in her letter that if Trump would not agree to reschedule the speech until the government reopens, he could deliver it from the Oval Office instead, a setting that would lack the grandeur of a congressional address.
Republicans cast her move as a ploy to deny Trump the stage.